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Delta (letter)

Delta (/ˈdɛltə/;[1] uppercase Δ, lowercase δ; Greek: δέλτα, délta, [ˈðelta])[2] is the fourth letter of the Greek alphabet. In the system of Greek numerals it has a value of 4. It was derived from the Phoenician letter dalet 𐤃.[3] Letters that come from delta include Latin D and Cyrillic Д.

"Δ" redirects here. For other uses, see ∆ (disambiguation).

A river delta (originally, the delta of the Nile River) is so named because its shape approximates the triangular uppercase letter delta. Contrary to a popular legend, this use of the word delta was not coined by Herodotus.[4]

Pronunciation[edit]

In Ancient Greek, delta represented a voiced dental plosive IPA: [d]. In Modern Greek, it represents a voiced dental fricative IPA: [ð], like the "th" in "that" or "this" (while IPA: [d] in foreign words is instead commonly transcribed as ντ). Delta is romanized as d or dh.

Change of any changeable quantity, in mathematics and the sciences (in particular, the [5][6]); for example, in the average change of y per unit x (i.e. the change of y over the change of x). Delta is the initial letter of the Greek word διαφορά diaphorá, "difference". (The small Latin letter d is used in much the same way for the notation of derivatives and differentials, which also describe change by infinitesimal amounts.)

difference operator

The :

Laplace operator

The of a polynomial equation, especially the quadratic equation:[7][8]

discriminant

The

area of a triangle

The of two sets.

symmetric difference

A in the value of a variable in mathematics or science.

macroscopic change

in a physical variable as seen in the uncertainty principle.

Uncertainty

An interval of possible values for a given quantity.

Any of the in particle physics.

delta particles

The determinant of the matrix of coefficients of a set of linear equations (see ).

Cramer's rule

That an associated number represents the location of a covalent bond in an organic compound, the position of which is variant between isomeric forms.

locant

A , simplicial complex, or convex hull.

simplex

In chemistry, the addition of heat in a reaction.

In , it represents a defendant.[9]

legal shorthand

In the financial markets, one of the , describing the rate of change of an option price for a given change in the underlying benchmark.

Greeks

A in jazz music notation.

major seventh chord

In , it can stand for a gene deletion (e.g. the CCR5-Δ32, a 32 nucleotide/bp deletion within CCR5).

genetics

The cites it (together with omicron for "odont") as the symbol of dentistry.[10]

American Dental Association

The anonymous signature of .[11]

James David Forbes

Determinacy (having a definite truth-value) in .

philosophical logic

In mathematics, the symbol ≜ (delta over equals) is occasionally used to define a new variable or function.

[12]

The uppercase letter Δ is used to denote:

A change in the value of a variable in

calculus

A in functional calculus

functional derivative

An auxiliary function in calculus, used to rigorously define the or continuity of a given function

limit

The in mathematics

Kronecker delta

The degree of a

vertex (graph theory)

The in mathematics

Dirac delta function

The transition function in

automata

in engineering mechanics

Deflection

The in actuarial science

force of interest

The of nuclear magnetic resonance in chemistry

chemical shift

The relative of different atoms in a molecule, δ being more electronegative than δ+

electronegativity

Text requiring deletion in ; the usage is said to date back to classical times

proofreading

In some of the manuscripts written by Dr. , the character of delta is used to represent Dee

John Dee

A subunit of the F1 sector of the

F-ATPase

The of an object in the equatorial coordinate system of astronomy

declination

The dividend yield in the option pricing formula

Black–Scholes

Ratios of , such as 18O/16O and D/1H from water are displayed using delta notation – δ18O and δD, respectively

environmental isotopes

The rate of depreciation of the aggregate capital stock of an economy in an in macroeconomics[13]

exogenous growth model

In a system that exhibits , the angle between voltage and current

electrical reactance

in chemistry

Partial charge

The maximum of a crystal in optical mineralogy.[14]

birrefringence

An voiced dental or alveolar fricative of uncertain articulation, the ancestor of the sound represented by Modern Irish dh

Old Irish

The lowercase letter δ (or 𝛿) can be used to denote:

Greek Delta / Coptic Dalda

These characters are used only as mathematical symbols. Stylized Greek text should be encoded using the normal Greek letters, with markup and formatting to indicate text style.

Arrow (symbol)

Chevron (insignia)

∆ (disambiguation)

D, d

Д, д

- Latin delta

- the partial derivative symbol, sometimes mistaken for a lowercase Greek letter Delta.

- the small eth appears similar to a small delta, and also represents a d sound in some contexts

ð

Th (digraph)

Thorn (letter)

Greek letters used in mathematics, science, and engineering

∇ -

Nabla symbol

Delta Air Lines

SARS-CoV-2 Delta variant